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AG will be negative and willapproach zero as the reaction proceeds because the actual concentrations of A and B will be getting smaller and the concentrations of C andD will be getting larger. Notice that when a reaction is at equilibrium,where there is no force driving the reaction in either direction and AGis equal to zero, Equation 13-3 reduces to0IAG°' = -RT In K'eqthe equation that, as we noted above (p. 368), relates the standardfree-energy change and the equilibrium constant.Even a reaction for which AG°' is positive can go in the forwarddirection, if AG is negative. This is possible if the term RT In([products]/[reactants]) in Equation 13-3 is negative and has a largerabsolute value than AG°'.
For example, the immediate removal of theproducts of a reaction can keep the ratio [products]/[reactants] wellbelow 1, giving the term RT In ([products]/[reactants]) a large, negativevalue.AGO/ and AG are expressions of the maximum amount of free energy that a given reaction can theoretically deliver. This amount ofenergy could be realized only if there were a perfectly efficient deviceavailable to trap or harness it. Given that no such device is available,the amount of work done by the reaction at constant temperature andpressure is always less than the theoretical amount.It is also essential to understand that some reactions that are ther-371372Part III Bioenergetics and Metabolismmodynamically favorable (i.e., for which AG is large and negative) nevertheless do not occur at measurable rates.
For example, firewood canbe converted into CO2 and H2O by combustion in a reaction that is veryfavorable thermodynamically. Nevertheless, firewood is stable foryears, because the activation energy (see Fig. 8-4) for its combustion ishigher than that provided by room temperature. If the necessary activation energy is provided (with a lighted match, for example), combustion will begin, converting the wood to the more stable products CO2and H2O and releasing energy as heat and light.In living cells, reactions that would be extremely slow if uncatalyzed are caused to occur, not by supplying additional heat but by lowering the activation energy with an enzyme (see Fig.
8-4). The freeenergy change AG/br a reaction is independent of the pathway by whichthe reaction occurs; it depends only on the nature and concentration ofthe initial reactants and the final products. An enzyme provides analternative reaction pathway with a lower activation energy, so that atroom temperature a large fraction of the substrate molecules haveenough thermal energy to overcome the activation barrier, and thereaction rate increases dramatically. Enzymes cannot change equilibrium constants; but they can and do increase the rate at which a reaction proceeds in the direction dictated by thermodynamics.Standard Free-Energy Changes Are AdditiveIn the case of two sequential chemical reactions, A 7—' B and B 7—'C, each reaction has its own equilibrium constant and each has itscharacteristic standard free-energy change, AGJ' and AG2'.
As the tworeactions are sequential, B cancels out and the overall reaction isA ^=±: C. Reaction A ^ ^ C will also have its own equilibrium constant and thus will also have its own standard free-energy change,AGtotai- The AG°' values of sequential chemical reactions are additive.For the overall reaction A ^=± C, AG^tai is the algebraic sum of theindividual standard free-energy changes, AGi' and AG2\ of the twoseparate reactions: AGtotai = AG?' + AG2'. This principle of bioenergetics explains how a thermodynamically unfavorable (endergonic) reaction can be driven in the forward direction by coupling it to a highlyexergonic reaction through a common intermediate.
For example, thesynthesis of glucose-6-phosphate is the first step in the utilization ofglucose by many organisms:Glucose + Pi> glucose-6-phosphate + H2OAG°' = 13.8 kJ/molThe positive value of AG°' predicts that under standard conditions thereaction will tend not to proceed spontaneously in the direction written. Another cellular reaction, the hydrolysis of ATP to ADP and Pi, isvery exergonic:ATP + H2O> ADP + PiAG°' = -30.5 kJ/molThese two reactions share the common intermediates Pi and H2O andmay be expressed as sequential reactions:(1)(2)Sum:Glucose + PjATP + H 2 OATP + glucose> glucose-6-phosphate + H2O> ADP + Pi> ADP + glucose-6-phosphateThe overall standard free-energy change is obtained by adding theAGO/ values for individual reactions:AG°' = +13.8 kJ/mol + (-30.5 kJ/mol) = -16.7 kJ/molChapter 13 Principles of BioenergeticsThe overall reaction is exergonic.
In this case, energy stored in thebonds of ATP is used to drive the synthesis of glucose-6-phosphate, aproduct whose formation from glucose and phosphate is endergonic.The pathway of glucose-6-phosphate formation by phosphate transferfrom ATP is different from reactions (1) and (2) above, but the netresult is the same as the sum of the two reactions.
In thermodynamiccalculations, all that matters is the initial and final states; the routebetween them is immaterial.We have said that AG°' is a way of expressing the equilibriumconstant for a reaction. For reaction (1) above,=qi[glucose-6-phosphate]=x 1Q_3^[glucose][Pi]Notice that H2O is not included in this expression. The equilibriumconstant for the hydrolysis of ATP isThe equilibrium constant for the two coupled reactions is_ [glucose-6-phosphate][ADP][Pi]eq3"[glucose][Pi][ATP]= (K'eqi)(K^q2) = (3.9 x 10" 3 M - 1 ) ( 2 .
0 x 105 M)= 7.8 x 102By coupling ATP hydrolysis to glucose-6-phosphate synthesis, the Keqfor formation of glucose-6-phosphate has been raised by a factor ofabout 2 x 105.This strategy is employed by all living cells in the synthesis ofmetabolic intermediates and cellular components. Obviously, thestrategy only works if compounds such as ATP are continuously available. In the following chapters we consider^several of the most important cellular pathways for producing ATP.Phosphate Group Transfers and ATPHaving developed some fundamental principles of energy changes inchemical systems, we can now examine the energy cycle in cells andthe special role of ATP in linking catabolism and anabolism (see Fig.1-13).
Heterotrophic cells obtain free energy in a chemical form by thecatabolism of nutrient molecules and use that energy to make ATPfrom ADP and Pi. ATP then donates some of its chemical energy toendergonic processes such as the synthesis of metabolic intermediatesand macromolecules from smaller precursors, transport of substancesacross membranes against concentration gradients, and mechanicalmotion. This donation of energy from ATP generally involves the covalent participation of ATP in the reaction that is to be driven, with theresult that ATP is converted to ADP and Pi or to AMP and 2Pi.
Wediscuss here the chemical basis for the large free-energy changes thataccompany hydrolysis of ATP and other high-energy phosphate compounds, and show that most cases of energy donation by ATP involvegroup transfer, not simple hydrolysis of ATP. To illustrate the range ofenergy transductions in which ATP provides energy, we consider thesynthesis of information-rich macromolecules, the transport of solutesacross membranes, and motion produced by muscle contraction.373O374Figure 13-1 The chemical basis for the large freeenergy change associated with ATP hydrolysis.(1) Electrostatic repulsion among the four negativecharges on ATP is relieved by charge separationafter hydrolysis.
(2) Inorganic phosphate (Pj) released by hydrolysis is stabilized by formation of aresonance hybrid (left), in which each of the fourP—0 bonds has the same degree of double-bondcharacter and the hydrogen ion is not permanentlyassociated with any one of the oxygens. (3) Theother direct product of hydrolysis, ADP2", alsoimmediately ionizes (right), releasing a proton intoa medium of very low [H+] (pH 7). A fourth factor(not shown) that favors ATP hydrolysis is thegreater degree of solvation (hydration) of the products Pj and ADP relative to ATP, which further stabilizes the products relative to the reactants.OOO-P-O-P-O-P-O—TRib N AdenineII1 1''4O"ATPH2Ohydrolysis, withrelief of charge repulsionooo~O—P—OH + H O - P - O — P - O O"\ AdenineADP 2 "O" O~resonancestabilization5"oQo8"jA T p 4oH+ + "0-P-O-P-O-H+O—P—(-liO"O"ADP 3 "p.2AG°' = -30.5 kJ/molThe Free-Energy Change for ATP HydrolysisIs Large and NegativeOOO"O—P—O—P— O—P—O-IO"Mg2IIO"0~OAdenineMgATP2"O"0—P—O—P—O-II°" p~MgADP"Figure 13—2 Formation of Mg2+ complexes partially shields the negative charges and influencesthe conformation of the phosphate groups in nucleotides such as ATP and ADPFigure 13-1 summarizes the chemical basis for the relatively large,negative, standard free energy of hydrolysis of ATP.
The hydrolyticcleavage of the terminal phosphoric acid anhydride (phosphoanhydride) bond in ATP separates off one of the three negatively chargedphosphates and thus relieves some of the electrostatic repulsion inATP; the Pi ( H P O 2 ) released by hydrolysis is stabilized by the formation of several resonance forms not possible in ATP; and ADP 2 ", theother direct product of hydrolysis, immediately ionizes, releasing H +into a medium of very low [H + ](~10~ 7 M).
The low concentration of thedirect products favors, by mass action, the hydrolysis reaction.Although its hydrolysis is highly exergonic (AG°' = -30.5 kJ/mol),ATP is kinetically stable toward nonenzymatic breakdown at pH 7 because the activation energy for ATP hydrolysis is relatively high. Rapidcleavage of the phosphoric acid anhydride bonds occurs only when catalyzed by an enzyme.Although the AG°' for ATP hydrolysis is -30.5 kJ/mol under standard conditions, the actual free energy of hydrolysis (AG) of ATP inliving cells is very different.
This is because the concentrations of ATP,ADP, and Pi in living cells are not identical and are much lower thanthe standard 1.0 M concentrations (Table 13-5). Furthermore, the cytosol contains Mg 2+ , which binds to ATP and ADP (Fig. 13-2). In mostenzymatic reactions that involve ATP as phosphoryl donor, the truesubstrate is MgATP2~ and the relevant AG°' is that for MgATP2" hydrolysis. Box 13-2 shows how AG for ATP hydrolysis in the intacterythrocyte can be calculated from the data in Table 13-4. AG for ATPhydrolysis in intact cells, usually designated AGP, is much more negative than AG°'; in most cells AGP ranges from - 5 0 to - 6 5 kJ/mol. AGPis often called the phosphorylation potential.
In the following discussion we use the standard free-energy change for ATP hydrolysis,because this allows convenient comparison with the energetics of othercellular reactions for which the actual free-energy changes within cellsare not known with certainty.Chapter 13 Principles of BioenergeticsBOX 13-2The Free Energy of Hydrolysis of ATP within Cells:The Real Cost of Doing Metabolic BusinessThe standard free energy of hydrolysis of ATP hasthe value -30.5 kJ/mol.
In the cell, however, theconcentrations of ATP, ADP, and Pi are not onlyunequal but are also much lower than the standard 1 M concentrations (see Table 13-5). Moreover, the pH inside cells may differ somewhat fromthe standard pH of 7.0. Thus the actual free energyof hydrolysis of ATP under intracellular conditions(AGP) differs from the standard free-energychange, AG0'.
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